Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of #1113⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×#1113⋊C3 |
| unambiguous semidirect product | #1113⋊C32 |
| unambiguous semidirect product | (C3×#1113)⋊C3 |
| Fitting, socle | C34 ⋊ A4 |
| derived | #1113 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #1113⋊C3 |
| commutator, cosocle, hypocenter | #1113 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C34 | A4 |
| LCS | G ▷ #1113 | |
| UCS | C1 ◁ C3 | |
124 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12 |
39 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 877);